Question

Swen and Raven went shopping with their individual money. If Swen gives $30 to Raven, then Raven will have twice the money left with Swen. But, if Raven gives $10 to Swen, then Swen will have three times as much as is left with Raven. How much money did Raven start with if she spent half her money on shopping?

a) $34
b) $68
c) $62
d) $128

Answer 1

If Raven spent half her money on shopping, she started with $126.

Step-by-step explanation:

Let's assume that Swen starts with a certain amount of money (x) and Raven starts with another amount of money (y).

According to the given information, if Swen gives $30 to Raven, then Raven will have twice the money left with Swen. This can be written as:

y + 30 = 2(x - 30)

Simplifying this equation, we get:

y = 2x - 90

Similarly, if Raven gives $10 to Swen, then Swen will have three times as much money as is left with Raven. This can be expressed as:

x + 10 = 3(y - 10)

Simplifying this equation, we get:

x = 3y - 20

Now, we have a system of linear equations:

y = 2x - 90

x = 3y - 20

Substituting the value of y from the first equation into the second equation, we get:

x = 3(2x - 90) - 20

Simplifying this equation, we get:

x = 6x - 270 - 20

5x = 290

x = 58

Substituting the value of x back into the first equation, we can find the value of y:

y = 2(58) - 90

y = 126

Therefore, Raven started with $126 if she spent half her money on shopping.